Rationalise the denominator of :
` ( 1) / ( sqrt 6 ) + ( 1)/( sqrt5 ) `

Answer

To rationalize the denominator of the expression \( \frac{1}{\sqrt{6}} + \frac{1}{\sqrt{5}} \), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{1}{\sqrt{6}} + \frac{1}{\sqrt{5}} \]

### Step 2: Find a common denominator
The common denominator for \( \sqrt{6} \) and \( \sqrt{5} \) is \( \sqrt{6} \cdot \sqrt{5} = \sqrt{30} \). We can rewrite each fraction with this common denominator.

### Step 3: Rewrite each term
We can express each term with the common denominator:
\[ \frac{1}{\sqrt{6}} = \frac{\sqrt{5}}{\sqrt{30}} \quad \text{and} \quad \frac{1}{\sqrt{5}} = \frac{\sqrt{6}}{\sqrt{30}} \]

### Step 4: Combine the fractions
Now, we can combine the two fractions:
\[ \frac{\sqrt{5}}{\sqrt{30}} + \frac{\sqrt{6}}{\sqrt{30}} = \frac{\sqrt{5} + \sqrt{6}}{\sqrt{30}} \]

### Step 5: Rationalize the denominator
To eliminate the square root in the denominator, we multiply the numerator and the denominator by \( \sqrt{30} \):
\[ \frac{\sqrt{5} + \sqrt{6}}{\sqrt{30}} \cdot \frac{\sqrt{30}}{\sqrt{30}} = \frac{(\sqrt{5} + \sqrt{6}) \cdot \sqrt{30}}{30} \]

### Step 6: Final expression
Thus, the rationalized form of the expression is:
\[ \frac{\sqrt{30}(\sqrt{5} + \sqrt{6})}{30} \]

### Final Answer
\[ \frac{\sqrt{30}(\sqrt{5} + \sqrt{6})}{30} \]

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